Wide-band phase-splitting network

ABSTRACT

A circuit is disclosed in which a quadrature coupler splits an applied signal into a pair of signals having a 90* phase differential therebetween. The pair of signals are applied to a pair of primary windings of a pair of transformers. The secondary windings of the transformers are connected in a T configuration. Three output signals are taken from the T-connected secondaries of the transformers each having exactly 120* relative phase with respect to each other. Equations are also disclosed describing the above circuit. A computer program is also disclosed for solving the equations enabling one of ordinary skill in the art to build multicoupled mode structures which provide various desired phase relationships.

United States Patent I [72] Inventor Richard V. Snyder 3,189,848 6/ 1965 Miyagi 333/9 X Glen Ridge, NJ. 3,428,920 2/ 1969 Oleksiak.... 333/6 X [21] Appl. No. 46,723 3,486,135 12/1969 Sweeney 333/9 [22] Wed June 1970 Primary Examiner-Herman Karl Saalbach [45] Patented Nov. 23, 1971 [73] Assignee Merrimac Research and Development Inc Amman Emmmer paul Gen'sler west CaldwelLNJ. Attorney-Lerner, Dav1d& Littenberg ABSTRACT: A circuit is disclosed in which a quadrature cou- [54] g g g NETWORK pler splits an applied signal into a pair of signals having a 90 phase difierential therebetween. The pair of signals are ap- [52] US. Cl 333/6, plied to a pair of primary windings of a pair of transformers. 333/10 The secondary windings of the transformers are connected in [51] Int. Cl. l-l0lp 5/12 a T configuration. Three output signals are taken from the T- [50] Field of Search 333/6, 8,9, connected secondaries of the transformers each having ex- 10 actly 120 relative phase with respect to each other. Equations are also disclosed describing the above circuit A [56] References cued computer program is also disclosed for solving the equations UNITED STATES PATENTS enabling one of ordinary skill in the art to build multicoupled 3,490,054 1/1970 Seidel 333/10 mode structures which Provide various desired Phase relationships.

RI R3 2/ SIGNAL GAIN GEN DEVICE C1 23 DIRECTIONAL COUPLER [8 a 4 GAIN i DEVICE c PATENTEBunv 23 I9?! LERNER, DAVID B LITTENBERG ATTORNEYS WIDE-BAND PHASE-SPLITTING NETWORK FIELD OF THE INVENTION This invention relates to a microwave phase splitter and particularly to a microwave splitter in which the phase relationship between output signals is determined by coupled modes of response of the phase splitter to applied signals.

BACKGROUND OF THE INVENTION Phase-splitting circuits of networks are devices which provide a number of output signals in response to an applied signal, each of the output signals having a fixed phase relationship with respect to the others. Many of the commonly thought-of phase-splitting circuits were developed long ago for driving power equipment such as three-phase motors. These devices, such as the well known Scott T were designed to operate at a single frequency (Le, 60 cycles per second) and at zero source impedance.

In the communications art phase splitters are also employed. Here, however, wide-band phase splitters are necessary. There are numerous circuits known in the mircowave art which divide an incident wide-band signal into two or more components whose relative phases are constrained to integer multiples of 11/2 radians. Included in this class are magic tees, split tees, quadrature hybrids. and ring hybrids. The relative output phases of the signals, supplied by these devices are determined by two coupled modes of operation of the device. Therefore, these output phase relationships are frequency-insensitive over an operating band of frequencies.

Combinations of these two coupled mode devices and other differential phase shift networks enable approximation of differential phase splits between signals at other than multiple of 11/2 radians. The combination devices are frequency-sensitive because they do not rely solely on couple-mode devices to provide the differential phase shifts.

The differential phase characteristic networks which are responsible for the frequency sensitivity of the combination device typically use polynomial or polynomial ratio approximations to ideal coupling characteristics which, in fact,.vary over a range as a function of frequency. The resultant phase vs. frequency response of the combination devices tend to ripple around the desired phase relationship, introducing harmonic distortion when passing wide-band signals.

BRIEF DESCRIPTION OF THE INVENTION In accordance with this invention, a phase-splitting device having first and second input ports and responding thereat to first and second input signals in three-coupled modes is driven by a second phase-splitting device which operates in two coupled modes.

This first phase-splitting device may be formed by a pair of transformers, the secondaries of which are interconnected to provide three-output ports. The primaries of the transformers are driven from the output ports of the second phase-splitting device. In this way, the drive to the primaries of the transformers have a fixed differential phase relationship therebetween over a frequency band so that the two transformers which in the present configuration have more than two coupled modes, provide three output signals which have a fixed differential phase relationship over this band of frequencies.

DESCRIPTION OF THE FIGURES The sole FIGURE is a schematic diagram of a circuit embodying the principles of this invention.

DETAILED DESCRIPTION OF THE INVENTION In the FIGURE, we see a circuit which includes a first transformer having a primary-to-secondary turns ratio of QM where Q and M are any number. A second transformer 11 is also shown having a primary to secondary turns ratio of PT, where P and T are any number. The secondary T of the transformer is tapped at a point 13 to provide K, turns on one side of the tap and K turns on the other.

One end 12 of the secondary of the transformer I0 is connected to the secondary of the transformer 11 at the point 13. A second end 14 of the secondary transformer 10 and ends 15 and 16 of the secondaries of transformer 11 serve as three outputs ports for the circuit shown in the FIGURE.

Three resistors are R,, R and R,, and are connected in a Wye configuration between the three output ports provided by the ends 14, I5 and 16 of the respective transformers.

By looking at the effect of applying a voltage across any one of the resistors R,, R or R,,, it is seen that no signal will be coupled to the primaries of either of the transformers 10 or 11 if the values of the resistors R,, R and R,,, the turns ratios of the transformers l0 and I1 and the placement of the point 13 on the secondary of the transformer 11 is chosen so that no net current will flow from the node formed by the junction of the three resistors R,, R and R,,. Therefore, it is intuitively seen that the structure shown in the FIGURE may in fact possess three independent coupled modes of operation when the parameters thereof are adjusted properly.

A directional coupler 17 having an input port, an isolated port, and first and second output ports drives the primaries of the transformers l0 and 11. A lead 18 connects one of the output ports of the coupler 17 through a gain device C to the primary of the transformer 10 while a lead 19 connects the second output port of the coupler 17 through a gain device C, to the transformer 11.

A signal generator 21 is connected by a lead 22 to the input port of the coupler 17. The isolated port of the coupler I7 is terminated in its characteristic impedance 23.

The gain devices C, and C, may provide increased signal amplitude or an attenuation thereof. The value C, or C by which the signal amplitudes are changed will effect the ultimate output signals provided by the circuit shown in the FIGURE.

In this embodiment the coupler 17 is a quadrature coupler operating in two coupled modes to provide output signals on the leads l8 and 19 having a differential phase relationship therebetween of over its frequency band of operation. It is important that the phase relationship between the signals applied to the primaries of transformers l0 and 11 be determined by the characteristics of the coupler l7 and not phase shifts picked up in the leads 18 and 19 unless the primary-tosecondary turns ratios of the transformers have an imaginary component. The imaginary component would be handled by inserting appropriate phase shifts between the signals on the leads l8 and 19. It should be clear that only small imaginary values can be handled this way without introducing undesirable phase ripple across the respective R,, R and R,,.

Therefore, the leads I8 and 19 are either kept very short or the phase response of both leads must be carefully matched. Of course phase shifts can be purposely introduced in the leads I8 and 19 to provide relative phase shifts in the signals applied to transformers l0 and II but these phase shifts should be relatively small, unless a frequency-sensitive response is acceptable.

The most common use to which the circuit shown in the FIGURE has been used thus far is for providing an output signal across each of the resistors R,, R and R,, having the same frequency content as the signal supplied by the signal generator 21 but each being separated by a relative I20 from one another. In such a case, the coupler 17 would be a 3 db. 0

quadrature coupler so that the signals on the leads 18 and 19 would equal in the frequency band of operation of the signal generator 21 and 90 out of phase with each other. The secondary of the transformer 11 would be center tapped so that K, i

and K would be equal, and the resistors R,, R and R would be of equal value. The gain elements C, and C would each have a value of one. The transformer ratios P:T and ():M

would be 0.720 and 0.817 respectively.

Various output phase shifts can be realized across the resistors R,, R and R,, by modifying the circuit parameters. Following are examples of various phase shifts which can be realized with the disclosed circuit. These parameters have been determined by solving the pair of equations (l6) and (I7) derived in Appendix A by using a computer program disclosed in Appendix B. It should be noted that examples 1, 2 and 3 require small imaginary turns ratios for the transformer 11. As pointed out previously, these are realized by introducing a phase shift between the leads l8 and 19. It should be noted that the imaginary part of the turns ratios are small compared with the real part so that the device still is not dominated by frequency-sensitive terms.

EXAMPLE l A circuit with the parameters listed below will produce relative output phases across the resistors R,, R and R of 209, 91 and 331 respectively with respect to the signal provided by the signal generator 21. The magnitude of the currents l l, and 1 following in the resistors R,, R, and R;, with respect to the current provided by the signal generator 21 will be 0.577, 0.566, and 0.589 respectively.

PARAMETERS:

Coupler l7; 3 db.

P:T=0.7220.004 i EXAMPLE 2 A circuit with the parameters listed below will produce relative output phases across the resistors R,, R and R of 206, 92 and 335 respectively with respect to the signal provided by the signal generator 21. The magnitude of the currents l,, l, and 1 following in the resistors R,, R, and R with respect to the current provided by the signal generator 21 will be 0.596, 0.520 and 0.61 1 respectively.

PARAMETERS:

Coupler l7; 3 db.

EXAMPLE 3 EXAMPLE 4 A circuit with the parameters listed below will produce relative output phases across the resistors R R, and R of 201,

90 and 321 respectively with respect to the signal provided by the signal generator 21. The magnitude of the currents 1,, l

and 1, following in the resistors R,, R, and R;, with respect to:

the current provided by the signal generator 21 will be 0.519, 0.580, and 0.625 respectively.

PARAMETERS:

Coupler l7; 3 db.

EXAMPLE 5 A circuit with the parameters listed below will produce relative output phases across the resistors R R and R, of 210, and 330 respectively with respect to the signal provided by the signal generator 21. The magnitude of the currents 1 1,, and 1,, following in the resistors R,, R, and R, with respect to the current provided by the signal generator 21 will be 0.408,

0.408, and 0.408 respectively.

PARAMETERS: Coupler l7; 3 db. K =K =l R,=l; R,==2; R =3 P:T=O.50l Q.-M=0.577

APPENDIX A For demagnetization of core Q-M, and for linear operation, Faradays Law of Induction yields the well-known flux continuous ampere-tums law (eq. 18). From this ampere-turns relationship derivable from Faradays Law with n in db.

n -(m) 1 P0 (fi) 3 1+ l 2 where K1 K T II: Ag"! t I Be I =C'e"' and 1 log 10 (2) At the junction of resistors R,, R, and R,, Kirchoff's Law requires l,+l- .+I,==0 (3) expanding (3 A(cos 0,+jsin0 )+B(cos 0 +jsin 9,)+C(cos0;,+jsin0,)==0 equating real and imaginary parts to 0.

Acos0 +Bcos0 +Ccos0 =0 Asin0,+Bsin6- ,+Csin0 =0 5 Hence A: B cos 0 -0 cos 0;

cos 6 or A: B sin 0 C sin 0;,

sin 0 Equating (6) and (7), and solving for C sin 0 cos 0; tan 6, cos 0;, tan 0 sin 0 (8) Now, reflectionless conservation of power requires (with unit input) 3 i: I R,=1

9 Hence A R +B Rg+C R3=1 (10) rewriting (8) C= K 8 where k sin fi -cos 0; tan 9;

1 cos 6 tan 0 -sin 0 (11a) Substituting (11) into (6) A: B cos 0 B [In] cos 0;

cos 6; (12) or 1 n q I log 5) B The ampere-turns law, referred to earlier, is

Li,,=!.1, l 8) where L inductance ip primary current is secondary current APPENDIX B To Be Run On An ].B.M. Model 360/65 1.0025 RA2=B'COS(A2) L.0029 Al l=-CMPLX(RAl.BAl)

1.0030 Al2=CMPLX(RA2.BA2)

1.0031 Al3==CMPl.X( RA3.BA31

1.0033 APOT=API(AKI+AK2) 1.0034 PRINT 4.AP.APOT.

QOM.A|I.AI2.AI3

1.0035 4 FORMAT(6GI4.6)

L.0036 6 FORMAT(G9.6)

1.0037 PRINT 101 1.003s 101 FORMAT ('MAGNITUDE 0F ll.l2.AND 13 ARE-' 1.0039 A11=cABs(AT1) 1.0040 Al2=CABS(Al2) 1.0041 Al3=CABS(Al3) 1.0042 PRINT l02.All.

Al2.Al3

1.0043 102 FORMAT(6G 17.0)

1.0044 READ(9,61CHK 1.004s IF (Cl-"(0.01

Go To 10 1.0046 END It should be understood that the above embodiments are merely illustrative of the principles of this invention and other embodiments will become obvious therefrom to those of ordinary skill in the art.

What is claimed is:

l. in combination: a first transformer having a primary and a secondary;

a second transformer having a primary and a secondary;

means for interconnecting said secondary of said first transformer and said secondary of said second transformer to provide first, second, and third output ports;

means responsive to an applied signal for providing first and second output signals; said signal providing means responding to said applied signal in two coupled modes so that said first and second output signals have a fixed differential phase relationship therebetween over a frequency band; and

means for applying said first and second output signals to drive said primaries of said first and second transformers respectively.

2. The combination as defined in claim 1 in which; said secondary of said second transformer has first and second ends and a center tap; said secondary of said first transformer has first and second ends; and said interconnecting means in-' clude means for connecting said first end of said secondary of said first transformer to said center tap of said secondary of said second transformer so that said second end of said secondary of said first transformer and said first and second ends of said secondary of said secondary serves as said first. second and third output ports respectively.

3. The combination as defined in claim 2 also including: first, second, and third impedance means connected between said first, second and third output ports; a signal generator for providing a wide-band signal; and means for applying said wide-band signal to said applied signal responsive means.

9. The combination as cm ifilainiialso flaming? a signal generator for providing a wide-band signal; and means for applying said wide-band signal to said applied signal-responsive means.

i i I t 7. The combination as defined in claim 6 also including: fixst, second and third impedance means connected between said first, second and third output ports. 8. The combination as defined in claim 7 in which said first, second and third impedances are equal in value. 

1. In combination: a first transformer having a primary and a secondary; a second transformer having a primary and a secondary; means for interconnecting said secondary of said first transformer and said secondary of said second transformer to provide first, second, and third output ports; means responsive to an applied signal for providing first and second output signals; said signal providing means responding to said applied signal in two coupled modes so that said first and second output signals have a fixed differential phase relationship therebetween over a frequency band; and means for applying said first and second output signals to drive said primaries of said first and second transformers respectively.
 2. The combination as defined in claim 1 in which; said secondary of said second transformer has first and second ends and a center tap; said secondary oF said first transformer has first and second ends; and said interconnecting means include means for connecting said first end of said secondary of said first transformer to said center tap of said secondary of said second transformer so that said second end of said secondary of said first transformer and said first and second ends of said secondary of said secondary serves as said first, second and third output ports respectively.
 3. The combination as defined in claim 2 also including: first, second, and third impedance means connected between said first, second and third output ports; a signal generator for providing a wide-band signal; and means for applying said wide-band signal to said applied signal responsive means.
 4. The combination as defined in claim 2 in which the differential phase shift introduced by said means for applying said first and second output signals to drive said primaries of said first and second transformer respectively, when converted to equivalent imaginary turns ratio for said second transformer is smaller compared to the real turns ratio thereof.
 5. The combination as defined in claim 4 in which said applied signal-responsive means is a quadrature coupler.
 6. The combination as defined in claim 5 in which said quadrature coupler is a 3 db. quadrature coupler.
 7. The combination as defined in claim 6 also including: first, second and third impedance means connected between said first, second and third output ports.
 8. The combination as defined in claim 7 in which said first, second and third impedances are equal in value.
 9. The combination as defined in claim 8 also including: a signal generator for providing a wide-band signal; and means for applying said wide-band signal to said applied signal-responsive means. 